F. Agüera

The accuracy of grid digital elevation models linearly constructed from scattered sample data

In this paper, a theoretical‐empirical model is developed for modelling the accuracy of a grid digital elevation model (DEM) linearly constructed from scattered sample data. The theoretical component integrates sample data accuracy in the model by means of the error‐propagation theory. The empirical component seeks to model what is known as information loss, i.e. the sum of the error due purely to sampling the continuous terrain surface with a finite grid interval and the interpolation error. For this purpose, randomly spaced data points, supposed to be free of error, were converted into regularly gridded data points using triangulation with linear interpolation. Original sample data were collected with a 2×2 m sampling interval from eight different morphologies, from flat terrain to highly rugged terrain, applying digital photogrammetric methods to large‐scale aerial stereo imagery (1 : 5000). The DEM root mean square error was calculated by the true validation method over several sets of check points, obtaining the different sampling densities tested in this work. Several empirical models are calibrated and validated with the experimental data set by modelling the DEM accuracy by combining two variables such as sampling density and a descriptive attribute of terrain morphology. These empirical models presented a morphology based on the product of two potential functions, one related to the terrain roughness and another related to the sampling density. The terrain descriptors tested were average terrain slope, standard deviation of terrain slope, standard deviation of unitary vectors perpendicular to the topographic surface (SDUV), standard deviation of the difference in height between adjacent samples in the grid DEM (SDHD), and roughness estimation by first‐, second‐, or third‐degree surface fitting error. The values obtained for those terrain descriptors were reasonably independent from the number and spatial distribution of the sample data. The models based on descriptors SDHD, SDUV, and standard deviation of slope provided a good fitting to the data observed (R 2>0.94) in the calibration phase, model SDHD being the one that yielded the best results in validation. Therefore, it would be possible to establish a priori the optimum grid size required to generate or store a DEM of a particular accuracy, with the saving in computing time and file size that this would mean for the digital flow of the mapping information in GIS.

Detecting greenhouse changes from QuickBird imagery on the Mediterranean coast

In this study a very high resolution image from the QuickBird satellite was used to detect new greenhouses built since the last update of the information system utilized for the study area. The area, located in the southeast of Spain, has the highest concentration of greenhouses in Europe, which makes it the heart of the economy of this region. The methodology proposed in this paper is based on the comparison of the classification of a current image with the information system corresponding to the last update. Maximum likelihood classification method was employed and different band combinations were used to define the training areas and to carry out the classification process. The optimal band combination for the detection of greenhouses was calculated by means of a variance analysis. The process was completed with the delineation of the new greenhouses with two algorithms programmed in Visual Basic 6.0, one to eliminate the loops shown around the greenhouses detected, and the other one, based on the Hough transformation, to delineate the contour of the polygons corresponding to the new greenhouses. The proposed methodology achieved (1) a value for true greenhouse surface of about 91.45% of the whole surface, (2) a very low value for undetected greenhouses (five greenhouses from a total of 202 that were built, representing 1.49% of the surface of new greenhouses), and (3) a low number of pixels wrongly classified as greenhouses.

Geometric accuracy assessment of the orthorectification process from very high resolution satellite imagery for Common Agricultural Policy purposes

This study has, as its main aim, the assessment of different sensor models to achieve the best geometric accuracy in orthorectified imagery products obtained from IKONOS Geo Ortho Kit and QuickBird basic imagery. The final orthoimages are compared, both geometrically and visually, with the panchromatic orthophotos based on a photogrammetric flight with an approximate scale of 1 : 20 000, which are now used for the European Union Common Agricultural Policy in Andalusia (Spain). Two‐dimensional root mean square (RMS2d) errors in independent check points are used as accuracy indicators. The ancillary data were generated by high accuracy methods: (1) check and ground control points (GCPs) were measured with a differential global positioning system and (2) an accurate digital elevation model was used for image orthorectification. Two sensor models were used to correct the satellite data: (1) a three‐dimensional (3D) rational function refined by the user with zero‐ (RPC0) or first‐(RPC1) order polynomial adjustment and (2) the 3D Toutin physical model (CCRS). For the IKONOS image, the best results in the final orthoimages (RMS2d of about 1.15 m) were obtained when the RPC0 model was used. Neither a large number of GCPs (more than nine), nor a better distribution of them, improved the results obtained with the RPC0. For the QuickBird image, the CCRS model generated the best results (RMS2d of about 1.04 m), although it was sensitive to the number and distribution of the GCPs used in its computation.

Accuracy assessment of digital elevation models using a non-parametric approach

This paper explores three theoretical approaches for estimating the degree of correctness to which the accuracy figures of a gridded Digital Elevation Model (DEM) have been estimated depending on the number of checkpoints involved in the assessment process. The widely used average‐error statistic Mean Square Error (MSE) was selected for measuring the DEM accuracy. The work was focused on DEM uncertainty assessment using approximate confidence intervals. Those confidence intervals were constructed both from classical methods which assume a normal distribution of the error and from a new method based on a non‐parametric approach. The first two approaches studied, called Chi‐squared and Asymptotic Student t, consider a normal distribution of the residuals. That is especially true in the first case. The second case, due to the asymptotic properties of the t distribution, can perform reasonably well with even slightly non‐normal residuals if the sample size is large enough. The third approach developed in this article is a new method based on the theory of estimating functions which could be considered much more general than the previous two cases. It is based on a non‐parametric approach where no particular distribution is assumed. Thus, we can avoid the strong assumption of distribution normality accepted in previous work and in the majority of current standards of positional accuracy. The three approaches were tested using Monte Carlo simulation for several populations of residuals generated from originally sampled data. Those original grid DEMs, considered as ground data, were collected by means of digital photogrammetric methods from seven areas displaying differing morphology employing a 2 by 2 m sampling interval. The original grid DEMs were subsampled to generate new lower‐resolution DEMs. Each of these new DEMs was then interpolated to retrieve its original resolution using two different procedures. Height differences between original and interpolated grid DEMs were calculated to obtain residual populations. One interpolation procedure resulted in slightly non‐normal residual populations, whereas the other produced very non‐normal residuals with frequent outliers. Monte Carlo simulations allow us to report that the estimating function approach was the most robust and general of those tested. In fact, the other two approaches, especially the Chi‐squared method, were clearly affected by the degree of normality of the residual population distribution, producing less reliable results than the estimating functions approach. This last method shows good results when applied to the different datasets, even in the case of more leptokurtic populations. In the worst cases, no more than 64–128 checkpoints were required to construct an estimate of the global error of the DEM with 95% confidence. The approach therefore is an important step towards saving time and money in the evaluation of DEM accuracy using a single average‐error statistic. Nevertheless, we must take into account that MSE is essentially a single global measure of deviations, and thus incapable of characterizing the spatial variations of errors over the interpolated surface.

Field evaluation of a self-propelled sprayer and effects of the application rate on spray deposition and losses to the ground in greenhouse tomato crops

BACKGROUND In the greenhouses of south-eastern Spain, plant protection products are applied using mainly sprayers at high pressures and high volumes. This results in major losses on the ground and less than uniform spray deposition on the canopy. Recently, self-propelled vehicles equipped with vertical spray booms have appeared on the market. In this study, deposition on the canopy and the losses to the ground at different spray volumes have been compared, using a self-propelled vehicle with vertical spray booms versus a gun sprayer. Three different spray volumes have been tested with a boom sprayer, and two with a spray gun. RESULTS The vehicle with the vertical spray boom gave similar depositions to those made with the gun, but at lower application volumes. Also, the distribution of the vertical spray boom was more uniform, with lower losses to the ground. CONCLUSIONS The vertical spray booms used in tomato crops improve the application of plant protection products with respect to the spray gun, reducing the application volumes and the environmental risks of soil pollution.

Relationship between atmospheric corrections and training-site strategy with respect to accuracy of greenhouse detection process from very high resolution imagery

Frequently, satellite images that are acquired to extract a target surface are atmospherically corrected prior to the detection process. Thus, the unification of measure units is achieved, and atmospheric effects are removed from various imagery sources or taken at different dates. In this paper, four increasing levels of atmospheric corrections are applied (Top-Of-Atmosphere transformation: TOA; Apparent Reflectance Model: ARM; Flat Areas Model: FAM; Non-Flat Areas Model: NFAM). Then, the classification process is carried out using two strategies of training-site definitions (statistically purified and crude training sites) and two satellite imagery sources (QuickBird and Ikonos). Three-way Analysis of Variance (ANOVA) tests and Fishers least-significant difference tests are included in quality classification assessment, based on four accuracy indexes. Two images from both remote sensors are orthorectified, and then it is checked that all selected atmospheric correction levels have significantly different influences on the statistics of both orthoimages. Taking into account the conditions established in this work, it is concluded that a lower atmospheric correction level would be preferred because it does not present significantly worse results than other levels considered. Training sites would not be statistically purified, and QuickBird or Ikonos would be chosen, depending on the aspect of the greenhouse detection accuracy preferred.

Geometric Accuracy Assessment of QuickBird Basic Imagery Using Different Operational Approaches

New very high-resolution space satellite images, such as QuickBird and Ikonos, open new possibilities in cartographic applications. This work has as its main aim assessment of a methodology to achieve the best possible geometric accuracy in orthorectified imagery products obtained from QuickBird basic imagery which will include an assessment of the methodology’s reliability. Root Mean Square Error (RMSE), mean error or bias, and maximum error in 79 independent check points are computed and utilized as accuracy indicators. Ancillary data was generated by high accuracy methods: 1) check and control points were measured with a differential global positioning system, and 2) a dense digital elevation model (DEM) with grid spacing of 2 m and RMSE-sub-z of about 0.31 m generated from a photogrammetric aerial flight at an approximate scale of 1:5000 that was used for image orthorectification. Two other DEMs with a grid spacing of 5 m and 20 m were also used. Four 3D geometric correction models were used to correct the satellite data: 2 terrain-independent rational function models refined by the user, a terrain-dependent model, and a rigorous physical model. The number and distribution of the ground control points (GCPs) used for the sensor orientation were studied as well, testing from 9 to 45 GCPs. The best results obtained about the geometric accuracy of the orthorectified images (2-D RMSE of about 0.74 m) were computed when the dense DEM was used with the 3-D physical and terrain-dependent models. The use of more than 18 GCPs does not improve the results when those GCPs are extracted by stratified random sampling.

A Theoretical Approach to Modeling the Accuracy Assessment of Digital Elevation Models

In this paper, a theoretical analysis is presented of the degree of correctness to which the accuracy figures of a grid Digital Elevation Model (DEM) have been estimated, measured as Root Mean Square Error (RMSE) depending on the number of checkpoints used in the accuracy assessment process. The latter concept is sometimes referred to as the Reliability of the DEM accuracy tests. Two theoretical models have been developed for estimating the reliability of the DEM accuracy figures using the number of checkpoints and parameters related to the statistical distribution of residuals (mean, variance, skewness, and standardized kurtosis). A general case was considered in which residuals might be weakly correlated (local spatial autocorrelation) with non-zero mean and non-normal distribution. Thus, we avoided the “strong assumption” of distribution normality accepted in some of the previous works and in the majority of the current standards of positional accuracy control methods. Sampled data were collected using digital photogrammetric methods applied to large scale stereo imagery (1:5 000). In this way, seven morphologies were sampled with a 2 m by 2 m sampling interval, ranging from flat (3 percent average slope) to the highly rugged terrain of marble quarries (82 percent average slope). Two local schemes of interpolation have been employed, using Multiquadric Radial Basis Functions (MRBF) and Inverse Distance Weighted (IDW) interpolators, to generate interpolated surfaces from high-resolution grid DEMs. The theoretical results obtained were experimentally validated using the Monte Carlo simulation method. The proposed models provided a good fit for the raw simulated data for the seven morphologies and the two schemes of interpolation tested (r 2 . 0.96 as mean value). The proposed theoretical models performed very well for modeling the non-gaussian distribution of the errors at the checkpoints, a property which is very common in geographically distributed data.

Assessing Geometric Reliability of Corrected Images from Very High Resolution Satellites

Since the launch of Ikonos by Space Imaging, LLC on 24 September 1999, the very high resolution (VHR) satellite imagery has been applied to diverse fields. Every application needs a certain geometric accuracy in the corrected image; therefore, the planimetric accuracy control of VHR satellite imagery proves to be fundamental. As a rule of thumb, the Root Mean Square error (RMS) computed at independent check points (ICPs) is the global measure most widely used for accuracy assessment in VHR imagery. This paper presents an assessment, focused on two QuickBird and Ikonos panchromatic single images, of the number of ICPs required to obtain an estimation of one-dimensional accuracy (RMS1d) with a certain confidence level or reliability. Thus, two theoretical approaches have been tested to estimate reliability depending on the number of ICPs, and they have been experimentally validated using the Monte Carlo simulation method. The residual’s samples were generated for both satellite images in the best possible operational conditions: (a) using optimal sensor models, (b) with high accuracy ground points measured by Differential Global Positioning System, (c) with an adequate number of well distributed ground control points (GCPs), and (d) using GCPs and ICPs well-defined on the raw images, i.e., with a reasonably low pointing error. Under these conditions, the two theoretical models tested provided a good fit (r 2 �97 percent) for the simulated data offered by Monte Carlo when outliers were withdrawn. There were no notable differences between the results obtained from the Ikonos and QuickBird scenes.

Atomization characteristics of hydraulic nozzles using fractal geometry

Fractal scalings of the V(x X) . Xd type have been used in this work for cumulative volume (V) distribution applied through spray nozzles in size x droplets, smaller than the characteristic size X. From exponent d, the fractal dimension (Df), which measures the degree of irregularity of the medium, has been deduced. This property consists of the repetition of the irregularity itself over a certain range of scales, and it is called self-similarity. The objects or sets that have this property are named fractals. Based on the considerations below, and supposing that the droplet set from a spray nozzle is self-similar, an algorithm has been developed to relate a nozzle type with a Df value. The data input for this algorithm were the droplet size spectra factors corresponding to 10%, 50%, and 90% (Dv0.1, Dv0.5, and Dv0.9, respectively) as measured at different operating pressures for different nozzle types. Multivariate, multilinear, and polynomial models were conducted to predict droplet size spectra factors based on Df and operating pressure (multilinear model) and based on Df, operating pressure, and orifice diameter (polynomial model). Df values showed dependence on nozzle geometry and independence of operating pressure. Significant coefficients of determination (r2) at the 95% confidence level were found for the fitted models. An exception occurred in one case, associated with Dv0.9. Thus, r2 values were higher for the polynomial models than for the multilinear models, except for a case associated with Dv0.1. These models could be useful to compare the behavior of different nozzles under the same operating conditions, or the same nozzle under different operating conditions. Because Df is related to nozzle geometry, the inclusion of Df in models to predict droplet size spectra factors will allow us to detect the geometric differences between nozzles, which are otherwise difficult to measure. Similar procedure could be carried out for other nozzles types.